﻿Many realistic networks can be characterized as complex networks and their scale-free features have been discussed to analyze their behaviors. A scale-free network is a network that has a power-law degree distribution. And it is thought to be robust to random attack, but an initial attack can also trigger global cascading failures. In this thesis, we study how cascading failures spread in a scale-free network with coupled map lattices model firstly. We propose a protection mechanism to block the cascading failures and limit the number of failed nodes. Online social network services have attracted more and more users in recent years. And they can also be modeled as scale-free networks. Hackers make the security in social networks a critical problem. In this thesis, we propose two virus propagation models to study the virus’ behavior in online social networks. One is based on the application network of Facebook, which is the most popular among these social network service providers. Another is based on an email virus propagation model, and we compare the behaviors of virus spreading in Facebook and the original email network. We find that, while Facebook provides a platform for application developers, it also provides the same chance for virus spreading. And virus will spread faster in Facebook network if its users spend more time on it.
Moreover, we study the group networks and application platform on Facebook. And we also propose a new virus propagation model and simulate it in a group network. We find that group networks have the scale-free features and an intentional attack or random multiple attacks can make most users in the group infected.